The stuff that's already cached needs to age out before it's replaced with files that have a "don't cache me" header on them.
As for the rest, it would be very odd for a shared hosting service to allow 777 file permissions; that's just asking to get pwned. (There
is a server configuration that allows it safely, but it has its own set of problems, and you'll rarely see it used outside of schools.) And the Free Hosting servers are locked down pretty tightly; anything that exposes the configuration is verboten, remote access is HTTP-only (though you can call HTTPS as a client), there are some fairly strict mod_security rules, and .htaccess options are limited (see
this sticky for more). That's the price you pay for free hosting on a service that doesn't want to be shut down by ISP blocks and blacklists every other day.